A person travels by car from one city to another with different constant speeds between pairs of cities. She drives for 24 min at 84 km/hr, 17 min at 101 km/hr, and 48 min at 50 km/hr. She spends 27 min eating lunch and buying gas.

*[*5:27 PM*]*

What is the average speed for the trip?

To calculate the average speed for the entire trip, we need to consider the total distance traveled and the total time spent driving. The time spent eating lunch and buying gas does not contribute to the distance, so we only consider the driving time.

### Step 1: Calculate the distance for each segment of the trip.
1. **First segment:**  
   \[
   \text{Distance} = \text{Speed} \times \text{Time}
   \]
   \[
   = 84 \, \text{km/hr} \times \frac{24 \, \text{min}}{60} \, \text{hr} = 84 \times 0.4 = 33.6 \, \text{km}
   \]

2. **Second segment:**  
   \[
   = 101 \, \text{km/hr} \times \frac{17 \, \text{min}}{60} \, \text{hr} = 101 \times 0.2833 = 28.6167 \, \text{km}
   \]

3. **Third segment:**  
   \[
   = 50 \, \text{km/hr} \times \frac{48 \, \text{min}}{60} \, \text{hr} = 50 \times 0.8 = 40 \, \text{km}
   \]

### Step 2: Calculate the total distance.
\[
\text{Total Distance} = 33.6 + 28.6167 + 40 = 102.2167 \, \text{km}
\]

### Step 3: Calculate the total driving time.
\[
\text{Total Time} = 24 \, \text{min} + 17 \, \text{min} + 48 \, \text{min} = 89 \, \text{min}
\]
Convert minutes to hours:
\[
\text{Total Time} = \frac{89 \, \text{min}}{60} = 1.4833 \, \text{hours}
\]

### Step 4: Calculate the average speed.
\[
\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{102.2167 \, \text{km}}{1.4833 \, \text{hours}} \approx 68.91 \, \text{km/hr}
\]

Thus, the average speed for the trip is approximately **68.91 km/hr**.

Would you like any further details on this calculation or have any questions?

---

Here are five related questions:
1. How would the average speed change if the person spent less time during the lunch break?
2. What is the impact of each driving segment on the overall average speed?
3. How does the choice of different constant speeds affect fuel efficiency?
4. Can we calculate the average velocity if the person returns to the starting point?
5. How would you convert the total distance traveled into miles?

**Tip:** When calculating average speed, always consider the total distance divided by the total time, regardless of the number of segments involved.

A person travels by car from one city to another with different constant speeds between pairs of cities. She drives for 24 min at 84 km/hr, 17 min at 101 km/hr, and 48 min at 50 km/hr. She spends 27 min eating lunch and buying gas. What is the average speed for the trip?

Learn how to calculate the average speed for a trip with multiple driving segments. This problem involves key mathematical concepts such as speed, distance, and time, and is suitable for students in Grades 8-10. Follow a step-by-step solution to find the average speed for the entire trip.

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